EFFECTIVE CONDUCTIVITY OF SUSPENSIONS OF OVERLAPPING SPHERES

An accurate first-passage simulation technique formulated by the authors [J. Appl. Phys. 68, 3892 (1990)] is employed to compute the effective conductivity sigma(e) of distributions of penetrable (or overlapping) spheres of conductivity sigma(2) in a matrix of conductivity sigma(1). Clustering of particles in this model results in a generally intricate topology for virtually the entire range of sphere volume fractions phi(2) (i.e., 0 less-than-or-equal-to phi(2) less-than-or-equal-to 1). Results for the effective conductivity sigma(e) are presented for several values of the conductivity ratio alpha = sigma(2)/sigma(1), including superconducting spheres (alpha = infinity) and perfectly insulating spheres (alpha = 0), and for a wide range of volume fractions. The data are shown to lie between rigorous three-point bounds on sigma(e) for the same model. Consistent with the general observations of Torquato [J. Appl. Phys. 58, 3790 (1985)] regarding the utility of rigorous bounds, one of the bounds provides a good estimate of the effective conductivity, even in the extreme contrast cases (alpha >> 1 or alpha congruent-to 0), depending upon whether the system is below or above the percolation threshold.